Critical computational analysis illuminates thereductive-elimination mechanism that activatesnitrogenase for N2 reductionSimone Raugeia,1, Lance C. Seefeldtb,1, and Brian M. Hoffmanc,1

aPhysical and Computational Sciences Directorate, Pacific Northwestern National Laboratory, Richland, WA 99352; bDepartment of Chemistry andBiochemistry, Utah State University, Logan, UT 84322; and cDepartment of Chemistry, Northwestern University, Evanston, IL 60208

Contributed by Brian M. Hoffman, September 11, 2018 (sent for review June 18, 2018; reviewed by Victor S. Batista, Michael B. Hall, and Frank Neese)

Recent spectroscopic, kinetic, photophysical, and thermodynamicmeasurements show activation of nitrogenase for N2 → 2NH3

reduction involves the reductive elimination (re) of H2 from two[Fe–H–Fe] bridging hydrides bound to the catalytic [7Fe–9S–Mo–C–homocitrate] FeMo-cofactor (FeMo-co). These studies rationalizethe Lowe–Thorneley kinetic scheme’s proposal of mechanisticallyobligatory formation of one H2 for each N2 reduced. They alsoprovide an overall framework for understanding the mechanismof nitrogen fixation by nitrogenase. However, they directly posefundamental questions addressed computationally here. We herereport an extensive computational investigation of the structureand energetics of possible nitrogenase intermediates using struc-tural models for the active site with a broad range in complexity,while evaluating a diverse set of density functional theoryflavors. (i ) This shows that to prevent spurious disruption ofFeMo-co having accumulated 4[e−/H+] it is necessary to include:all residues (and water molecules) interacting directly with FeMo-covia specific H-bond interactions; nonspecific local electrostatic in-teractions; and steric confinement. (ii) These calculations indicatean important role of sulfide hemilability in the overall conversionof E0 to a diazene-level intermediate. (iii ) Perhaps most im-portantly, they explain (iiia) how the enzyme mechanisticallycouples exothermic H2 formation to endothermic cleavage ofthe N≡N triple bond in a nearly thermoneutral re/oxidative-addition equilibrium, (iiib) while preventing the “futile” gener-ation of two H2 without N2 reduction: hydride re generatesan H2 complex, but H2 is only lost when displaced by N2, toform an end-on N2 complex that proceeds to a diazene-levelintermediate.

nitrogenase | mechanism | DFT | computation

Biological nitrogen fixation is one of the most challengingchemical transformations in biology, the conversion of N2 to

ammonia. The catalyst for biological N2 fixation, the metal-loenzyme nitrogenase, is known in three different forms (1) withthe most abundant being the Mo-dependent enzyme, which iscomposed of the electron-donating Fe protein and the catalyticMoFe protein. The Fe protein, a homodimer, delivers oneelectron at a time during transient association with the MoFeprotein heterotetramer with dissociation of the two proteinsdriven by the hydrolysis of two ATP to two ADP/Pi per electrontransfer (ET) event (2). The reduction of N2 takes place on the[7Fe–9S–Mo–C–homocitrate] FeMo-cofactor (FeMo-co) in theactive site of the MoFe protein (Fig. 1), with the [8Fe–7S] P-cluster in the MoFe protein acting as an ET intermediary.Lowe and Thorneley put forward a kinetic model for catalysis

by the MoFe protein, including rate constants for formation ofeach intermediate state, designated as En, where n indicates thenumber of electrons and protons accumulated. This scheme in-corporates a controversial limiting stoichiometry:

N2 + 8e− + 16ATP+ 8H+ → 2NH3 +H2 + 16ADP+ 16Pi, [1]

with an obligatory formation of 1 mol of H2 per mole ofN2 reduced, and a corresponding requirement of 8[e−/H+],not 6, and as a result, the apparently “wasted” hydrolysis of4 ATP (3–5).In recent years, we have demonstrated (6, 7) that this stoi-

chiometry arises because activation of nitrogenase for N2 re-duction involves the accumulation of four reducing equivalentsat the active-site FeMo-co (4) to form a state with two [Fe–H–

Fe] bridging hydrides and two sulfur-bound protons, denotedE4(4H), the Janus intermediate, and that breaking the N≡Ntriple bond requires the reductive elimination (re) of H2 fromE4(4H) (6–9). This process corresponds to the forward directionof the equilibrium in Fig. 2, which leads to the formation of adiazene-level N2 reduction product [denoted as E4(2N2H)]; thereverse of this reaction is the oxidative addition (oa) of H2 withrelease of N2 (6). EPR/electron nuclear double resonance(ENDOR) and photophysical measurements established re/oaas central to the mechanism of the wild-type enzyme and showedit to be a nearly isoergic (ΔG = −8 kJ/mol), kinetically ac-cessible process (8, 9). Photophysical measurements furthersuggested that during re activation of nitrogenase, E4(4H) andE4(2N2H) are likely connected via an H2-bound intermediate[E4(H2)] (9). These studies provide an overall framework for un-derstanding the mechanism of nitrogen fixation by nitrogenase.

Significance

This report critically evaluates the mechanism by which ni-trogenase cleaves the N≡N triple bond. It assesses the ther-modynamic driving force provided by the accompanying,apparently “wasteful,” reductive elimination of an H2, andexplains how the enzyme mechanistically couples exothermicH2 formation to endothermic triple-bond cleavage in a nearlythermoneutral equilibrium process, thereby preventing the“futile” generation of two H2 without N2 reduction. This eval-uation rests on a critical assessment of the density functionaltheory flavors needed to properly treat nitrogenase, and ademonstration that to prevent spurious disruption of FeMo-coupon 4[e−/H+] accumulation, one must employ a nitrogenasestructural model that includes all residues interacting directlywith FeMo-co, either via specific H-bond interactions, non-specific electrostatic interactions, or steric confinement.

Author contributions: S.R., L.C.S., and B.M.H. designed research; S.R. performed research;S.R., L.C.S., and B.M.H. analyzed data; and S.R., L.C.S., and B.M.H. wrote the paper.

Reviewers: V.S.B., Yale University; M.B.H., Texas A&M University; and F.N., Max PlanckInstitute for Bioinorganic Chemistry.

Conflict of interest statement: B.M.H. and F.N. are coauthors on a 2017 research article.

Published under the PNAS license.1To whom correspondence may be addressed. Email: simone.raugei@pnnl.gov, lance.seefeldt@usu.edu, or bmh@northwestern.edu.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1810211115/-/DCSupplemental.

Published online October 24, 2018.

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However, they directly pose a number of fundamental questionsthat are addressed computationally in this report. First, we ad-dress the “protonation isomers” at the E4 level of electron ac-cumulation, in particular the disposition of the two [Fe–H–Fe]moieties of the mechanistically central E4(4H) intermediate. Thiscontentious question has not been resolved experimentally, andits computational examination has required us to carry out acritical evaluation of the computational methodology required tostudy the nitrogenase catalytic mechanism. Computational stud-ies of nitrogenase (10–22), mostly based on broken-symmetry(BS) density functional theory (DFT), have provided a wealthof information about the electronic structure of the FeMo-co(resting) state E0 (14, 15). However, early work was con-strained by the uncertainty as to the existence/identity of thecofactor central atom, and the limited size of the structuralmodels adopted (10–13, 16, 18). Recently, computational inves-tigations have begun to use larger structural models of the cat-alytic pocket (20, 21, 23–27). However, these included studiesaddressing the structure of E4(4H) that advanced novel mecha-nistic proposals that are difficult to reconcile with the chemicalexpectations and experimental evidence. Notably, work by Siegbahn(20, 23), Rao et al. (21), and McKee (22) suggested the pro-tonation of the FeMo-co central carbon atom during catalysis,while Siegbahn (20, 23) even proposed a Fe-bound methyl in-termediate as the central E4 catalytic species. Very recently,Einsle and coworkers (28) were able to solve the structure of theas-isolated VFe protein and observed replacement of the S2Bsulfide that bridges Fe2–Fe6. This led them to propose the twohydrides of E4(4H) state bridge the Fe2–Fe6 center, and that thisis the state that reductively eliminates H2, leaving a vacantbinding site for N2. This proposal likewise needs computationalassessment.

To evaluate these proposals and in so doing answer funda-mental questions of nitrogenase catalysis, we have carried out anin-depth evaluation of a variety of DFT flavors, structuralmodels, and oxidation states of the resting state, and show thatthe proper incorporation of all interactions with the proteinenvironment that envelops FeMo-co at the enzyme active site iscritical to stabilize FeMo-co and prevent its disruption uponprotonation. The resulting structural model is then used tocharacterize the alternative E4 “protonation isomers,” including,but not limited to, characterization of the ground-state structureof E4(4H). In doing this, we are led to consider the hemilabilityof Fe–S bonds during catalysis (28–30).With this foundation, we are able to answer two of the key

unresolved mechanistic questions: (i) what is the overall ther-modynamic driving force for the process by which ATP-coupledelectron delivery (Eq. 1) leads to N2 reduction with loss of H2 atthe E4 mechanistic stage; (ii) how does the enzyme mechanisti-cally prevent the even more favorable production of a second H2without reduction of N2, namely, how is re of H2 mechanisticallycoupled to cleavage of the N≡N triple bond.

Computational MethodsStructural Models. The FeMo-co strongly interacts with the sur-rounding protein environment mostly via hydrogen bonding andelectrostatic interactions. Therefore, any quantitative computa-tional investigation of its activity must include a realistic repre-sentation of the enzymatic pocket. In particular, as shown in Fig.1, in addition to the coordination bonds with ligands, Fe1-α-275Cys, Mo-α-442His (Azotobacter vinelandii numbering) (2),and Mo-R-homocitrate, FeMo-co engages several hydrogenbonds with the protein backbone, side chains, and water mole-cules present in the enzymatic pocket, which are known to beabundant near the FeMo-co (31). Some of these interactions arenot evident from a simple investigation of the available crys-tallographic structures, as they are a representation of themost populated configuration at the temperature at whichthey were solved (typically 100 K). At room temperature, amultitude of local minima very close in free energy are ac-cessible, and this conformational complexity finely tuneschemical reactivity.In the present work, we use a structural model of nitrogenase

based on submicrosecond force-field–based molecular dynamics(MD) simulations (32). The model includes all of the residuesinteracting directly with FeMo-co both via specific H-bond in-teractions and nonspecific electrostatic interactions (Fig. 1),while the rest of the protein is described with a polarizablecontinuum (33). Five different structural models of decreasingcomplexity were examined (SI Appendix, Fig. S1).Model (a).The full model (a) includes the FeMo-co with truncatedmodifications of the α-275Cys, α-442His ligands (Azotobactervinelandii numbering), R-homocitrate, and all of the MoFeprotein residues and water molecules that engage hydrogen-bonding interactions with the FeMo-co, or are known to beimportant of the catalytic activity (α-70Val and α-96Arg). Cysteine,histidine, arginine, valine, and R-homocitrate residues were

Fig. 1. Structure of the FeMo-co binding pocket as obtained from MDsimulations (22) (A) and schematic representation of FeMo-co (standardatom numbering) (B). For simplicity, only the polar H atoms are shown. Thecolor coding of atoms is as follows: rust, Fe; yellow, S; cyan, C; purple, Mo;red, O; blue, N; light gray, H. Hydrogen bonds are shown as thin red sticks.The cartoon representation of the protein in cyan color is reported with thepurpose to highlight the surrounding protein environment. The N2 accesschannel is indicated with the thick blue arrow.

N2 H2

N2 H2

re

oa

E (4H) E (2N2H)

2N2H

Fig. 2. Schematic of the reductive-elimination (re)/oxidative-addition (oa)mechanism. 2N2H indicates a diazene-level N2 reduction product.

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modeled as methylthiolate, imidazole (or 4-methyl-imidazole),methylguanidinium, and tert-butyl and dimethyl glycolate, re-spectively. Recent reports highlighted that the protonation stateof the homocitrate may influence the electronic properties ofFeMo-co (24, 25). In the present study, homocitrate was con-sidered fully deprotonated. Arginines were considered pro-tonated, whereas the effect of both neutral (δ- and e-form) andprotonated forms of α-442His was explored. The backbone ofα-356Gly, α-357Gly, 358Leu, and α-359Arg, which interacts withFeMo-co via N–H hydrogen bonds, was modeled as a methyl-ammine terminated triglycine. α-278Ser forms hydrogen bondswith FeMo-co with both the side chain and the backbone N–H,and it was included in full as C-methylated serine. The stericconfinement exerted by the protein matrix on α-70Val andα-96Arg was included by adding one ethane molecule next toα-70Val at the location of the backbone C atoms of α-66Gly, theside chain of α-98Asn, the backbone of α-70Val and α-69gly, and abridging water molecule (SI Appendix, Fig. S1A). It is importantto point out that it is crucial to include the residues aroundα-70Val and α-96Arg to avoid unrealistic, large conformationalreorganization of residues as observed in other reports (20, 23).The C atoms of the ethane molecule were kept fixed at theirequilibrium distance. The atoms at the locations where the resi-dues were truncated were also fixed during the geometry opti-mizations. The list of the frozen atoms is provided in SI Appendix,section S7.Starting from the full model (a), we generated four additional

models by progressively deleting residues, as follows.Model (b). Model (b) deletes all water molecules interacting withFeMo-co (SI Appendix, Fig. S1B).Model (c). Model (c) further deletes the backbone of α-356Gly,α-357Gly, 358Leu, and α-359Arg (SI Appendix, Fig. S1C).Model (d). Model (d) additionally omits the side chain and thebackbone N–H of α-278Ser (SI Appendix, Fig. S1D).Model (e). Model (e) further removes the residues α-70Val, α-96Arg,and α-359Arg, yielding a minimal model that includes only FeMo-coand its ligands α-275Cys, α-442His, and Mo-R-homocitrate (SIAppendix, Fig. S1E).The initial position of atoms was obtained from previous MD

simulation studies (32). Specifically, we performed a clusteringanalysis of the MD trajectory to find groups of similar frames,and then adopted the frame closest to the center of the largestgroup (representing about the 80% of the configurational spaceof the residues included in the quantum-mechanical model). Therepresentative MD configuration we adopted for the presentstudy contains the same number of water molecules present inthe starting Protein Data Bank (PDB) structure (2). The validityof the adopted structural model is discussed in detail below. Wewill show that it is imperative to include all of the residuesinteracting with FeMo-co, that is, model (a), to obtain mean-ingful mechanistic predictions. In particular, the protein cagehelps stabilize the FeMo-co and avoid artifacts such as thosereported in recent investigations, where the protonation of thecentral carbide up to CH3 (20, 23), with consequent disruption ofthe cofactor, was found very favorable and erroneously proposedto be a key catalytic step.

Electronic Structure Calculations.BS-DFT. It is commonly accepted that BS-DFT calculations rep-resent a good compromise between computational efficiency andaccuracy, and DFT has been widely applied to the study ofFeMo-co. Noodleman and coworkers (14) reported an exhaus-tive search for the lowest-energy electronic wavefunction ofFeMo-co in the S = 3/2 E0 state for a minimal active-site model,which corresponds to model (e) described above, including onlyFeMo-co and its ligands. It was shown that, as expected, the E0(S = 3/2) state maximizes the antiferromagnetic couplingbetween the Fe centers. Later, Harris and Szilagyi (16) showed

that both pure generalized gradient approximation (GGA) andhybrid functionals consistently reproduce Noodleman’s results.Recent large-scale calculations carried out by Bjornsson andcoworkers (26, 27) corroborated these early studies. We notethat, although BS-DFT is effective in resolving the questions ofnitrogenase function addressed here, the approximate nature ofthe adopted functionals, coupled with the single determinantframework of the theory, is unable to capture finer quantitativedetails associated with the complex transformations at the FeMo-co,as noted below.For each En, there are various possible patterns that maximize

the antiferromagnetic coupling, which are in the absence of thepotential due to the protein environment equienergetic. Theasymmetry of the protein environment breaks the degeneracy ofthese spin patterns. As shown in SI Appendix, Fig. S2, the energydifference between patterns can be as high as 23 kJ/mol for E0. Similardifferences are found for the other En states investigated. In the fol-lowing, for each En, the lowest energy spin pattern was adopted.The present DFT calculations explored seven exchange and

correlation functionals: BP86, BLYP, PBE, B3LYP, PBE0, M06,and M06-2X, primarily focusing on the GGA BP86 (34–36)functional and the hybrid B3LYP functional (37–39). However, aresult discussed without explicit mention of functional is derivedwith BP86 for reasons discussed in SI Appendix, section S3. TheAhlrichs VTZ basis set was used for all Fe atoms (40), the LosAlamos National Laboratory basis set LANL2TZ with an ef-fective core potential was employed for the Mo atom (41), andthe 6-311++G** basis set was employed for all atoms coordinatedto metal atoms, including protic and hydridic hydrogen atomsand all of the atoms with which they interact via a covalentbond or a hydrogen bond, and finally the 6-31G* basis set (42)was adopted for all other atoms. All calculations were per-formed with the NWChem quantum chemistry package (43).Oxidation state.Various different oxidation states for Fe centers ofthe FeMo-co in the E0 (S = 3/2) have been proposed over theyears. There is now general consensus (27, 44) that the properoxidation state of E0 is [Mo3+3Fe2+4Fe3+]. The majority of thecalculations presented in this work were performed on E0 in thisoxidation state. However, for a better assessment of the generalvalidity of our results, selected E0 and E4 species were also in-vestigated for an electron counting corresponding to the moreoxidized E0 (S = 3/2) state, [Mo3+1Fe2+6Fe3+]. The currentconsensus is that FeMo-co in E0 has a low-spin Mo(III) (27, 44),consistent with ENDOR measurements that show small hyper-fine couplings to 95Mo (27). In all of our calculations on E0, Mohas a very low spin density, regardless of the exchange andcorrelation functional that is adopted (as described directly be-low) (SI Appendix, Tables S2 and S3). In E4, we again find a Mo(III) oxidation state, but the metal ion can assume low- or high-spin configurations depending on the location of the hydrogenatoms and the functional employed, with GGA functionals (e.g.,BP86) preferentially yielding low spin configurations (low spindensities) and hybrid functionals (e.g., B3LYP) favoring highspin states (higher spin densities; SI Appendix, Tables S4–S11).95Mo ENDOR experiments on E4(4H) have shown small 95Mocouplings in E4, little changed from the Mo hyperfine couplingin E0, which not only implies the persistence of the Mo(III)oxidation state, but also suggests that the low spin state persistsas well (45, 46). In that sense, the ENDOR measurements supportthe choice of the GGA functionals as being most appropriatefor the present investigation.Spin states. Spectroscopic investigations have provided the spinstate of various intermediates in the Lowe–Thorneley kineticmodel, notably for this report, E0, E2, and both E4(4H) andE4(2N2H). As recently established (47), not only E0 but also theE2 intermediates have a total spin S = 3/2, while the two E4intermediates have S = 1/2 (6). Therefore, calculations were

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performed for the observed S = 3/2 spin state (E0 and E2) andthe two S = 1/2 (E4) states within the BS approach (16). Be-cause of the single-determinant nature of BS-DFT, what iscalculated are not the pure S = 3/2 or S = 1/2 spin states, butrather a mixed determinant with MS = 3/2 or MS = 1/2 compo-nents (27, 44). This is an important point that should be kept inmind, as the energies of the proper pure spin states can be quitedifferent from the BS-DFT energies. Clearly, all of the manyDFT studies reported in the literature suffer from the sameproblem. The energy of the pure spin states can be estimatedusing the Heisenberg spin ladder framework (14, 15, 48–50),which might be problematic for the FeMo-co because of thelarge exchange coupling constants (14, 15). A few recent pio-neering studies point the way beyond DFT in addressing thenitrogenase problem (51–53). Conclusions drawn below aretempered by this recognition. For a more straightforwardcomparison between computation and experiment, we will stillrefer to the S = 3/2 and S = 1/2 state for E0 and E4, rather thanMS = 3/2 and MS = 1/2, respectively.Initial guesses were constructed according to the spin config-

urations of SI Appendix, Table S1 from atomic guesses corre-sponding to Fe2+ (S = 2), Fe3+ (S = 5/2), and Mo3+ (S = 3/2;different choices yielded similar results). Three BS solutionswere shown to maximize the antiferromagnetic coupling be-tween spins in the E0 (S = 3/2) state [see SI Appendix, Fig. S2,corresponding to the state BS7 proposed by Noodleman andcoworkers (14)]; initial geometries were optimized for the anti-ferromagnetic coupling with the lowest energy (16, 27). Then, foreach En state and its isomers that are considered (see below), allof the 35 possible BS solutions were explored at both BP86 andB3LYP level (SI Appendix, Table S1). There are eight magneticcenters in FeMo-co (1Mo3+, 3Fe2+, and 4Fe3+). In the absenceof an external magnetic field, we can set the spin of one of thecenters (for instance, Mo) arbitrarily either up or down, whichleaves a total of 7!/(4!·3!) = 35 possible spin up and spin downcombinations for both S = 1/2 and 3/2 total spin states, if we donot distinguish the specific location of Fe2+ and Fe3+ centers.For a more detailed discussion, see ref. 27. Finally, the geometryof the BS solutions within 20 kJ/mol from the lowest-energysolution was further optimized for E0, the first four lowest-energy E4 protomers, the protonated CH E4 isomer (see below),and all of the diazene-level N2 reduction E4 states.Medium effects. The COSMO polarizable dielectric continuum(33) was used to describe the protein environment not explicitlyconsidered in our structural models along with atomic radiiaccording to ref. 54. A dielectric continuum should be alwaysused with care, as the dielectric properties of a protein are illdefined. Ideally, one could assume that the larger the adoptedstructural model is, the smaller the dependence on the dielectricconstant of the continuum. In the present work, two dielectricconstants were examined, e = 4 and 10. As shown in SI Appendix,the energy differences between E4 isomers calculated with ourlargest structural model show little dependence (smaller than10 kJ/mol) on the choice of e, in contrast to what observed forthe smaller models, where far larger variations are observed. Thisresult suggests that the residues included in our largest modelindeed well describe the local environment of FeMo-co. All of theenergies discussed in this paper are calculated for e = 4, as wethink this is more appropriate to describe the hydrophobic pro-tein scaffold beyond the outer coordination sphere of FeMo-co.Free-energy corrections. Free-energy corrections were estimatedusing harmonic vibrational frequencies after projecting out thespurious imaginary frequencies associated with the frozen atomicpositions.Exploration of possible pathways for interconversion of E4 isomers and H2

release. The size of the working structural model [model (a)]precluded a full transition state search based on vibrationalfrequencies. We estimated the energetic barrier associated with

equilibria between the lowest-energy E4 isomers, E4(4H),E4(4H)(b), E4(4H)(c), and E4(2H;H2), using a simple linesearch based on constrained geometry optimizations, wherebya given Fe/H distance is gradually varied between the limitingvalues assumed in two targeted E4 species. In a similar man-ner, we studied the release of H2 from E4(2H,H2) and E4(2H,H2;N2) by a stepwise increase of the distance between Fe2 andthe center of mass of the H2 molecule. In all of the cases, foreach targeted distance, the position of all atoms was relaxed,except for the atoms at the truncation points, as discussed inStructural Models above.

ResultsWe investigated five structural models of the nitrogenase activesite [models (a) to (e)], with the extent of incorporating inter-actions with the protein environment pictured in Fig. 1 in-creasing in the order, model (e) → model (a), using a variety ofDFT flavors, various protonation states of FeMo-co, as well asdifferent oxidation states for E0. The majority of the calculationswere performed starting from the electron count associated withthe “oxidized”Mo3+3Fe2+4Fe3+ E0 (S = 3/2) oxidation state withα-195His doubly protonated. The latter choice was based on pKavalues estimates for the doubly protonated α-195His higher than10. The pKa of α-195His was estimated from the free energy fortransferring either the e- or δ-proton for the protonated α-195His

to histidine in water, for which an accurate value of the pKa isavailable. This calculation was performed using our largestmodel. For completeness, selected structures were also analyzedfor the more oxidized [Mo3+1Fe2+6Fe3+] E0 (S = 3/2) state andfor neutral α-195His.The structure and the corresponding energetics of various

critical E4 protonation states were calculated at both BP86 andB3LYP level of theory. We found that the two functionals pro-vide a similar picture of the energy landscape of the E4 isomers;differences will also be discussed. Because BP86 predicts a low-spin Mo(III) state for both E0 and E4, consistent with theavailable ENDOR data and X-ray/computational studies (27,44), as well as for other reasons to be given below, the energiesdiscussed here refer to this functional unless noted; B3LYPenergies are nonetheless given as appropriate. A detailed dis-cussion on the performance of these and other functionals ispresented in SI Appendix, section S3.Because of the large number of possible isomers, the energetic

comparisons mostly included only the total electronic energy andcontinuum corrections for the protein environment, that is,without including zero-point energy and vibrational correctionsto free energy, as their inclusion would have required compu-tationally very expensive vibrational frequency calculations for alarge number of structures. Rather, frequency calculations wereperformed only on the low-lying intermediates of mechanisticsignificance.

Protonation States of E4. Previous computational studies on asimplified model of nitrogenase (19), which included only FeMo-co and its ligands, revealed that μ2-S atoms are preferentiallyprotonated over μ3-S atoms and that accumulation of [e−/H+]pairs starting from E0 proceeds by the alternate protonation ofμ2-S atoms and Fe atoms. Examination of a number of possibleprotonation states for the extended model (a) confirmed theseinitial observations. The relative energetics and the structure ofall of the E4 states we analyzed is reported in SI Appendix, Fig.S3, while the states relevant to the present discussion are listed inFig. 3. The computations here performed on model (a) indicatethat, among the three μ2-S atoms, protonation of S5A and S2B(located on the reactive face; Fig. 1) is more favorable than theprotonation of S3A, which is located in a protein matrix cleft andreceives hydrogen bonds from the protein backbone (Fig. 1).There are three low-lying E4 states that differ by the location of

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one hydride (Fig. 3). Consistent with low-temperature ENDORresults (6, 7), and in keeping with previous exploratory calcula-tions (9), the lowest-energy state has two hydrides asymmetricallybridging Fe2–Fe6 and Fe3–Fe7, and two protonated sulfur atoms(S5A and S2B). We will refer to this state as E4(4H).The next state, indicated as E4(4H)(b), lies only ΔE = 4.8 kJ/mol

higher then E4(4H), and differs from it in that the Fe2–H–Fe6bridging hydride has migrated to Fe2 in E4(4H)(b), with Fe6 thusbinding a terminal hydride and acting as one terminus of the hy-dride bridge. Next higher in energy (ΔE = 10.5 kJ/mol) is adihydride species E4(4H)(c) with both hydrides bridging the Fe2–Fe6 centers, similar to the E4 intermediate recently proposed byEinsle for the FeV-cofactor in the vanadium nitrogenase (28).Slightly higher in energy still (ΔE = 16.3 kJ/mol) we found adihydrogen intermediate E4(2H;H2) with a strongly activateddihydrogen moiety [d(H–H) = 1.00 Å, vs. 0.7 Å for the isolatedmolecule] located on Fe2.As schematically depicted in Fig. 3, the E4 isomers containing

two hydrides bound in some way to the Fe2 have the Fe2–S2Bbond broken or partially broken. In addition, E4(4H)(c) Fe2–Fe6dibridged dihydride has a very elongated Fe6–S2B bond [2.72 Åvs. 2.32 and 2.48 Å in E4(4H) and E4(4H)(b), respectively]. In thenext section, we will comment on the possible role of the hemilabileFe–S bond(s) in the activity of nitrogenase. Addition of disper-sion corrections (55–57) has only a minimal effect on this ladderof states. For instance, the relative BP86-D3 (56, 57) energies of thefour low-energy E4 states are 0, 12.2, 14.3, and 20.7 kJ/mol. AtB3LYP level of theory, only E4(4H), E4(4H)(c), and E4(2H;H2) wereidentified as lowest-energy isomers. Instead, E4(4H)(b) was foundto be unstable. Indeed, geometry optimizations started from theE4(4H)(b) BP86 structure yielded either the E4(2H;H2) state, whichis located at +27.5 kJ/mol above E4(4H), or the E4(4H)(c), which isnearly degenerate with the E4(4H) being located at only 2.8 kJ/molabove it. A simple line search for a possible pathway connectingthese states carried out at the BP86 level of DFT indicates that themigration of the hydride between Fe3 and Fe7 in the lowest-lyingE4(4H) to Fe2 of E4(4H)(b) (ΔE‡ ∼ 29 kJ/mol), and of one of thetwo hydrogens between Fe2 and Fe6 in E4(4H)(b) to Fe2 in E4(4H)(b)

[ΔE‡ ∼ 14 kJ/mol relative to E4(4H)] is facile.In computations with the large model (a) of Fig. 1, we found

that protonation of the central carbide, with the concomitantformation of a deformed E4(3H,CH) FeMo-co state (Fig. 4 andSI Appendix, Fig. S3), is extremely unfavorable (ΔE = +121.4 kJ/mol).Using hybrid functionals, such as B3LYP, the energy of E4(3H;CH)

decreases considerably but still remains far above E4(4H) (ΔE =+81.6 kJ/mol). Also for this isomer, addition of dispersion cor-rections (55–57) has only a small effect. For example, the BP86-D3 energy relative to E4(4H) is +106.6 kJ/mol. This finding is incontrast to recent reports by Siegbahn (20, 23), Rao et al. (21),and McKee (22) that E4(3H;CH) is lower in energy than E4(4H)(20–23). Frequency calculations on the first four low-energystates E4(4H), E4(4H)(b), E4(4H)(c), and E4(2H;H2) allowed esti-mation of free energies, and confirmed the relative ordering dis-cussed above, and locate E4(4H)(b), E4(4H)(c), and E4(2H;H2) atΔG = 4.1, 13.6, and 8.8 kJ/mol above the E4(4H) baseline, re-spectively, as shown in Fig. 3.Geometry optimizations of these states with neutral, rather

than protonated, α-195His provide similar qualitative ordering,but with E4(4H)(b), and E4(2H;H2) located only at ΔE = 4.1 and8.3 kJ/mol from E4(4H). Finally, analysis of E4(4H), E4(4H)(b),E4(2H;H2), and E4(3H,CH) based on the assumption that theresting-state E0 (S = 3/2) exhibits an electron count corre-sponding to the oxidation state [Mo3+1Fe2+6Fe3+] provided asimilar energy ordering with E4(4H)(b), E4(2H;H2) at only ΔE =5.7 and 7.1 kJ/mol above E4(4H), while E4(3H,CH) is more thanΔE = 140 kJ/mol above E4(4H).Taken altogether, our computations show that likely there are at

least four low-lying E4 isomers in equilibrium with each other.Although the energy difference between them is small and wellwithin typical DFT errors, the finding that the state with the lowestenergy has two [Fe–H–Fe] bridging hydrides, E4(4H), is consistentwith the conclusion from low-temperature ENDORmeasurements(6), while the characterization of a low-lying H2 complex, E4(2H;H2), possibly involved during reductive elimination of the hy-drides of E4(4H), is consistent with recent photophysical studiesshowing that re of H2 involves such a complex (8, 9).

Role of the FeMo-Co Environment. The major improvement in thepresent computations compared with other recent mechanisticstudies (20–23) is that we incorporated the entire protein envelopearound FeMo-co, including the full set of hydrogen-bonding inter-actions from both protein residues and water molecules (Fig. 1).To obtain a detailed understanding of the importance of the differentinteractions, we examined structural models (b) through (e) ofprogressively decreasing complexity (Fig. 4). These unambiguouslyshows that the local environment around FeMo-co plays a cru-cial role in stabilizing the cofactor and controlling the reactionpathway.

Fig. 3. Relative free energy (black) and energy (red) of various E4 species potentially involved in FeMo-co reductive activation and the breaking of the N2

triple bond. Protic and hydridic hydrogens are indicated in green and red, respectively.

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SI Appendix, Fig. S1 depicts the five levels of incorporating theprotein environment of FeMo-co adopted in the present work:(i) represents the full (largest) model employed in our study,which includes all residues enclosing FeMo-co (see Methods forlisting), and, in particular all of the residues interacting via H-bonding and electrostatic interactions (Fig. 1); (ii) eliminates thewater molecules interacting with FeMo-co; (iii) additionallyeliminates the backbone of the residues H-bonded to the bottom ofFeMo-co; (iv) also removes the side chain and the backbone N–Hof α-278Ser, thus eliminating most of the H bonds to FeMo-co;and (v) shows a minimal model, which includes only the cofactorand its ligands. The models adopted by Siegbahn (20, 23) andRao et al. (21) are similar to our models (c) and (d), in that theylack the majority of the H-bond cage around FeMo-co, whileMcKee’s model (22) is identical to our minimal model (e). Inparticular, although Rao et al. (21) performed a multiscalequantum-chemical study that included the full protein scaffold,they still missed the majority of the active-site interactions, asthey simply adopted one of the available X-ray structures andneglected the presence of water, which is known to be presentnear the FeMo-co (31). Any realistic model must include hy-drogen bonding from water as well as the protein residues, andmost of the H-bonding network becomes apparent only aftercomputationally relaxing the protein in its aqueous environ-ment at room temperature. The representative MD configu-ration (32) we adopted in the present study contains the samenumber of water molecules present in the starting PDB struc-ture (2). However, in our model, FeMo-co has been evolvedaccording to MD simulations during which hydrogen bondsform the water molecules and protein residues; the most rep-resentative configuration has been chosen for the calculation asdescribed in Computational Methods.As shown in Fig. 4, with the resulting full model (a), the

native-like FeMo-co core of E4(4H) is about 98 kJ/mol (BP86) or62 kJ/mol (B3LYP) more stable than the (deformed) C-protonatedE4(3H,CH) core at this level of [e−/H+] accumulation. The pro-gressive elimination of protein cage around the cofactor reversesthe order; elimination of the five water molecules present on one ofthe FeMo-co sides lowers the gaps between E4(4H) and E4(3H,CH)to 75 kJ/mol (BP86) or 53 kJ/mol (B3LYP) in favor of E4(4H).Removal of the backbone chain on the bottom of the cofactor inmodel (c) (i.e., opposite to the FeMo-co Fe2,3,6,7 catalytic face)makes E4(3H,CH) more stable than E4(4H) by 35 kJ/mol (BP86).Elimination of α-278Ser (which engages H bonds with FeMo-cotrough the side-chain OH and the backbone NH) in model (d)brings the energy gap to 119 kJ/mol (BP86) or 89 kJ/mol (B3LYP)in favor of the E4(3H,CH); the situation is even more extremewith the minimal model (e), where the open core is over 120 kJmore stable at both BP86 and B3LYP levels of theory. Fromthe trend of the relative stability of E4(4H) to E4(3H;CH), it isevident that all of the residues at the active site play an im-

portant stabilizing role on E4(4H). Although the progression ofFig. 4 presents a clear trend in the energetics, which shows theopen core to be irrelevant to function, quantitatively, even theseresults might not yet be at convergence. In all likelihood, moreextended models should be used to properly describe the highlyanisotropic protein environment beyond the second coordinationsphere of the FeMo-co, as included in the present study. Indeed,it has been shown for other systems, such as the photosystem II(58–60), that the field arising from the highly heterogeneousprotein scaffold finely tunes activity.We note that Siegbahn’s original model (20) corresponded

roughly to our model (d), but in a recent communication (23), heextended his initial structural model to match the size of ourlargest model, in response to some experimental data from ourteam suggesting an equilibrium involving a dihydrogen species[the E4(2H;H2) species discussed below] (9). The results with thelarger model repeated Siegbahn’s former observation of a fa-vorable protonation of the central carbon. However, althoughthe size (number of atoms) of his expanded model (23) is com-parable with ours, this new model is fundamentally identical tothe original one (20) in that it does not incorporate crucial in-teractions with the protein residues and water molecules aroundthe FeMo-co core; the additional residues are only around thehomocitrate tail. Thus, our study demonstrates that it is only thefailure to incorporate the protein envelope encapsulating FeMo-co that results in an open FeMo-co core upon [e−/H+] delivery,and that inappropriately appears to make protonation of thecentral carbon atom thermodynamically favorable.However, what is the actual role of the protein environment?

To what degree are the H-bonding interactions energeticallystabilizing the core of the reduced FeMo-co, and to what degreedoes the protein confining cage stabilize its geometry? To bettercharacterize which effect dominates, for each of the models (a)to (d), we removed all of the protein residues and water mole-cules and recalculated the energies without relaxing the geom-etries of FeMo-co (SI Appendix, Fig. S4). Indeed, using thegeometry of FeMo-co from models (a) and (b), we obtain thatE4(4H) is still more stable than E4(3H;CH) by ΔE(el) = 105.8 and89.8 kJ/mol (BP86), respectively (difference in the total energywithout PCM corrections); in contrast, using the geometry ofFeMo-co from model (c), which lacks the protein residues onthe bottom of the FeMo-co, we obtain the reverse result withE4(3H;CH), now more stable than E4(4H) by ΔE(el) = 63.3 kJ/mol.In model (d), the stability of FeMo-co from model E4(3H;CH)relative to that of E4(4H) increases to 151.9 kJ/mol, a value that isclose to the value obtained directly with model (e), with FeMo-coof E4(3H;CH) more stable than that of E4(4H) by ΔE(el) =132.4 kJ/mol. Regarding the FeMo-co geometry itself, goingfrom model (a) to model (e), a contraction of the majority ofthe Fe–S distances is observed for E4(4H) (up to 4% for theFe1–S1A and Fe7–S4B), while an expansion of most of the Fe–S

Fig. 4. Effect of the enzymatic environment around FeMo-co on the relative stability of the bridging hydride state E4(4H) and C-protonated state E4(3H,CH).(A) Models used in the present study, with the labels of the residues sequentially removed from the full model (a): highlighted in blue [model (b)], green[model (c)], red [model (d)], and black [model (e)], respectively (SI Appendix, Fig. S1). (B) Corresponding relative electronic energy (no polarizable continuumcorrections applied) as obtained from DFT/BP86 and DFT/B3LYP level of theory (values in parentheses).

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distances is observed for E4(3H;CH) (up to 3% for Fe3–S5Aand Fe6–S1B).Remarkably, the change in the difference in energies between

FeMo-co in the E4(4H) and E4(3H;CH) states with the modeloccurs almost exclusively through changes in the energy ofE4(3H;CH); the energy of E4(4H) is rather insensitive to the sizeof the model, varying by less than 20 kJ/mol passing from model(a) to model (e). This can be clearly appreciated from the datareported in SI Appendix, Fig. S4, where the energy of FeMo-co inthe E4(4H) and E4(3H,CH) states as obtained from the fivemodels studied here are compared with that of FeMo-co in theE0. These results indicate that the protein envelope is (as mighthave been expected) complementary to the geometry of theclosed-core FeMo-co observed in the resting state, and that theprotein scaffold enforces this geometry upon FeMo-co all alongthe catalytic cycle, quite likely with the benefit that it preventsthe enzyme from destroying its active-site cluster through carbideprotonation to form CH4. Our analysis indicates that all of theprotein envelope around of FeMo-co is responsible for the sta-bilization of E4(4H) over E4(3H;CH), but with a more prominentrole of the residues on the bottom, which appear to structurallyconfine the cofactor, preventing the decomposition upon re-duction seen in the computations that do not include them (20,23). Further details of the role of the protein environment instabilizing the cofactor and determining the actual mechanism ofN2 reduction are presented in SI Appendix.

Fe–S Bond Hemilability. We analyzed the structures of all fourlowest-energy E4 electron-accumulation isomers, E4(4H), E4(4H)(b),E4(4H)(c), and E4(2H;H2), which are very close in energy, and inaddition the structure of E4(3H;CH). As can be seen from SI Ap-pendix, Table S13, all of the bond distances for FeMo-co in the E4states are similar to those in E0, with two notable exceptions. Thefirst one is the expected marked elongation in Fe3–C and Fe7–Cdistances in the extremely high-energy E4(3H;CH) species (1.6 and1.3 Å relative to E0, respectively) as a consequence of the disruptionof FeMo-co upon protonation of the central carbon. In contrast, forall of the species that are potentially energetically accessible andmechanistically important, the Fe–C bond lengths change by lessthan 0.1 Å relative to E0. In short, in energetically accessible states,the Fe–C bonds are maintained.The second exception is the Fe2–S2B bond for some isomers

with protonated S2BH. Generally, we observe that protonation ofan S atom bound to two metal ions causes a maximum increaseof the Fe–S bonds of 0.1–0.2 Å, while protonation of an S atombound to three metal ions causes a maximum lengthening of theFe–S bond up to 0.4 Å. In keeping with this behavior, in E4(4H)where Fe3/Fe7 is bridged both one of the two bridging hydridesand by the protonated S5B, the Fe3–S5B bond elongates by 0.2 Åand the bond to Fe7 by less than 0.1 Å. The second hydride ofE4(4H) bridges Fe2/Fe6, as does the protonated S2B. However, incontrast, the Fe2–S2B bond in E4(4H) elongates by almost 0.4 Å.This bond is actually broken in the low-energy isomers E4(4H)(b),E4(4H)(c), and E4(2H;H2), with the Fe2–S2B distance increasedby about 1.6 Å in these cases. Higher-energy isomers again arecharacterized by an increase of the Fe2–S2BH bond distance, inline with the other Fe–S bonds of S bound to two metal ions. Inthe double-bridged Fe2/Fe6 dihydride E4(4H)(c), also the Fe6–S2Bdistance considerably elongates, being about 0.40 Å longer thanin E4(4H). The behavior of the Fe6–S2B in E4(4H)(c) is even moredramatic at the B3LYP level of theory, whereby the Fe6–S2BHbond further elongates and, when 195His doubly protonated, theS2BH deprotonates and H2S is formed upon proton transfer from195His, which remains coordinated to Fe6. Release of S2B (asHS−) via the formation of a doubly bridged Fe2/Fe6 dihydride,similar to E4(4H)(c), has been recently proposed to be central forN2 activation in vanadium nitrogenase (28).

What differentiates the behavior of S5B and S2B in E4(4H) islikely to be in some part the presence of the H bond to S2B from195His; in the low-lying states with broken Fe–S2B bond, rear-rangement of the bridging hydrides makes S2B unique. We hy-pothesize that, as proposed for some H2-producing catalytic systems(29, 30), the hemilability of the Fe–S2B bond is important to creatingan efficient H2 re pathway with the concomitant binding of N2in which Fe2 first binds both hydrides, and then forms H2. Weconclude, anticipating the results presented in the next sec-tion, that upon release of H2 and binding of N2, the Fe2–S2Bbond is restored. The reversible breaking of this Fe–S bondfurther demonstrates its hemilabile nature. To the best of ourknowledge, this behavior of the Fe–S bond in nitrogenase hasbeen proposed previously only by Einsle and coworkers (28).

Thermodynamics of N2 Activation. It is possible to achieve a pro-found understanding of the thermodynamic necessity of couplingH2 formation via re to cleavage of the N≡N triple bond by lookingat the overall process for the formation of any of the diazene-levelintermediates [E4(2H;N2), E4(H;N2H), or E4(NHNH)] from E0.Focusing just on the formation of E4(NHNH), as displayed in Fig. 5,the overall process is exergonic by ΔGE4 = −103 kJ/mol at pH 7 (adetailed discussion on how this value was calculated is presented inSI Appendix, section S5). What makes this process so favorable canbe understood by decomposing it into the two parts shown in Fig. 5:(i) the endergonic formation of E4(NHNH) from E0, N2, 2H

+, and2e−, the latter provided by the Fe protein and the hydrolysis of fourATPs, with ΔGDZ = +67 kJ/mol; and (ii) the exergonic formationof H2 from 2H+, and 2e−, again provided by the Fe protein withATP hydrolysis, with ΔGH2 = −170 kJ/mol. Thus, although directformation of E4(NHNH) without generation of H2 is thermo-dynamically unfavorable, nitrogenase couples this unfavorablereaction of N2 with a highly favorable one, generation of H2,resulting in an overall exergonic process to drive N2 fixation.Following Bucket and Thauer (61), this process may thereforebe viewed as “cluster-based electron bifurcation,” in which twohydride electron pairs split, with an exergonic reaction involvingone pair (H2 formation) driving an endergonic reaction involvingthe other (N2 triple-bond cleavage).

N2 Activation by Reductive Elimination.MD simulations (32) showedthat access of small substrates to the active site is very facile andsuggested that N2 and H2 are always present in the catalyticpocket near the Fe2–Fe6 edge confined by α-70Val and α-195His.Guided by these simulations, possible N2 binding sites were ex-plored for the four low-lying E4(4H), E4(4H)(b), E4(4H)(c), andE4(2H;H2) isomers, using the BP86 functional. First, geometry

Fig. 5. The energetics of formation of E4(NHNH) from the enzymatic reac-tants and its decomposition into two individual two-electron, two-protonprocesses, each involving the hydrolysis of 2ATP: N2 binding and formationof E4(NHNH); release of H2 formed by re from E4(4H). These are coupledthrough displacement by N2 of the H2 formed by re.

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optimizations were performed constraining the N2 molecule tostay at a Fe–N2 distance typical of metal–N2 molecular com-plexes. Then the structures were relaxed without the constraint.All attempts to find a stable N2-bound state to either E4(4H),E4(4H)(b), or E4(4H)(c) failed. In contrast, E4(2H;H2), resultingfrom the reductive formation of H2, with retention of the H2bound to the doubly reduced FeMo-co core, reacts with N2 toform a asymmetrically bridged, end-on Fe2–(N2)–Fe6 adduct,E4(2H;H2;μ-N2), reminiscent of the side-on, end-on N2 bridgingmode reported for a few classes of complexes (62, 63). TheE4(2H;H2;μ-N2) state is ΔG = 29.2 kJ/mol above E4(4H) (Fe2–N and Fe6–N distances of 1.87 and 2.07 Å, respectively) (Fig.3). Upon formation of E4(2H;H2;μ-N2), the H2 becomes lessactivated, with the H–H distance shortening from 1.00 Å inE4(2H;H2) to 0.84 Å and a concomitant reduction of the Fe2–S2B bond of 0.2 Å. Release of H2 from E4(2H;H2;μ-N2), yieldingthe E4(2H;N2) state with N2 bound end-on to Fe2 and resto-ration of the Fe2–S2B bond, is thermodynamically favorable(ΔG = −33.7 kJ/mol; Fig. 3).The energy barrier for H2 release from both E4(2H;H2) and

E4(2H;H2;μ-N2) was estimated using the line search approachdiscussed in Methods. A monotonic increase of energy wasobtained when exploring elimination of H2 from E4(2H;H2) withthe search carried out until the energy had increased by over50 kJ/mol, increasing the Fe2–H distance from its equilibriumvalue of about 1.5 to 3.5 Å. This is a consequence of the highenergy of the E4(2H)* FeMo-co state, with its doubly reduced Fecore produced by H2 loss. In short, the H2-bound state, E4(2H;H2), is readily formed by re of the two hydrides of E4(4H), butit does not release that H2. In contrast, a barrier of only about28 kJ/mol was estimated for H2 release from E4(2H;H2;μ-N2)when using the same constrained optimization approach, with anestimated Fe2–H2 distance at the transition state of 2.1 Å (SIAppendix, Fig. S5). Although at this point the computations do notdefinitively discriminate between a concerted and stepwise pro-cess, the striking difference observed between E4(2H;H2;μ-N2)and E4(2H;H2) offers an explanation for the experimental reportof an H2 complex as an intermediate in re, with H2 lost only uponN2 binding. The computations also explain the implication drawnfrom HD formation during turnover under N2 and D2, that H2 isreleased only concomitant with binding of N2 (4, 8, 9).The pictorial representation of all of the states discussed

here is shown in SI Appendix, Fig. S6, and an animation pro-vided as Movie S1 illustrates the proposed overall process of reof the hydrides to form H2, followed by the described reactionwith N2 leading to release of the H2. Although, as noted, thedata reported in Fig. 3 are obtained at BP86 level, the B3LYPfunctional provides a consistent picture (SI Appendix, Fig. S7).To understand the role of re, we further analyzed the bonding

and the electron distribution in the various E4 species. Previousanalysis of the electronic properties of the E2(2H) state (19),carried out within the natural bond orbital (NBO) framework(64, 65), indicated that the Fe–H can be described as polarizedcovalent bonds, with charge buildup on the H atom of about −0.2e,as expected from the difference in electronegativity of the atomsinvolved. The same is true for the E4(4H) and E4(4H)(b) in-termediates. Nonetheless, as shown in SI Appendix, Fig. S4, thetwo Fe–H bonds in E4(4H) and E4(4H)(b), whether involvingbridging or terminal hydrides, each can be viewed as two-electron covalent bonds that together store the four re-ducing equivalents. As also discussed in SI Appendix, Fig. S4,upon formation and release of H2, two electrons are firststored in and then depart with the H2 molecule. This processleaves two reducing equivalents (i.e., electrons) on the FeMo-co core, which is at the heart of the re mechanism (6, 7, 9): asthe H2 molecule forms, two reducing equivalents become

available for binding and activating N2, explaining why onlyE4(2H; H2) is able to bind N2.The NBO analysis indicates that in this double adduct, the

two remaining reducing equivalents are distributed within theFeMo-co core, primarily on the Fe; the Mo valency does notchange. The N2 moiety receives a fraction of the reducing equiva-lents via π-acceptor (FeMo-co-to-N2) interactions: N2 assumes anoverall net negative charge of −0.29 e, nearly equally distributedbetween the two N atoms. Extension of the NBO analysis to theend-on Fe2–(N2) moiety (62) of E4(2H;N2) reveals that the bondbetween Fe2–(N2) is characterized by negligible σ-donor interac-tions (N2-to-FeMo-co) and large π-acceptor (FeMo-coto-N2) in-teractions. Thus, according to the NBO formulation, the σ-chargetransferred from N2 to FeMo-co is about 0.01 e, while the chargebacktransferred to N2 because of π-acceptor effects is 0.29 e, whichresults in a large net fractional negative charge on N2 (−0.41 eaccording to NBO atomic charge partitioning). The N–N bonddistance in E4(2H;N2) is d(N–N) = 1.14 Å, only 0.04 Å longer thanin the free molecule (SI Appendix, Fig. S6). This contrasts with thebond elongation observed in typical metal dinitrogen complexes,where N–N is considered “strongly” activated at d(N–N) >1.20 Å (66). However, in contrast to the majority of the modeldinitrogen complexes, protonation of the distal N atom inE4(2H;N2) is thermodynamically accessible, being endergonicby 24.2 kJ/mol, while no protonation of the proximal N atomwas found. We do not discuss the protonation mechanism ofN2, which is the subject of an ongoing investigation. However,our analysis suggests that the first proton most likely is deliveredby the protonated S2B, which in turn is promptly reprotonated byα-195His, the first of two instances in this investigation where thisresidue acts as a proton “buffer” (see below). We remark thathistidine is often used to rapidly shuttle protons in enzymes, aprototypical example being carbonic anhydrase (67).Upon N2 protonation, the N–N distance increases to 1.27 Å

and the N2H moves from Fe2 to a bridging position between Fe2and Fe6 (SI Appendix, Fig. S6). The second protonation of N2 isexergonic by ΔG = −12.4 kJ/mol, with the resulting transdiazene-bound intermediate E4(η2-NHNH) + H2 located at ΔG =+1.4 kJ/mol from E4(4H) + N2. The diazene moiety asymmet-rically binds side-on between Fe2 and Fe6 with Fe2–N1, Fe2–N2,and Fe6–N2 distances of about 1.92, 1.88, and 1.96 Å. Re-markably, the N–N distance (1.39 Å) is considerably longer thanthe distance in the isolated transdiazene molecule (1.25 Å) cal-culated at the same level of theory.On the basis of these purely thermodynamics considerations,

the present calculations suggest that formation of the dihydrogenadduct E4(2H;H2), followed by N2 binding and loss of H2, leadsto a diazene-level intermediate E4(2N2H) with an overall equilibriumfree energy consistent with the experimental free-energy change ΔGof approximately −8 kJ/mol (8). Thus, depending on which of the twoE4(2N2H) isomers is the equilibrium product of the re of H2 andbinding of N2, the computations yield the following (Fig. 3):

E4ð4HÞ+N2 ⇄E4ð2N2HÞ+H2;ΔG=−4.5  kJ=mol  or  1.4  kJ=mol. [2]

The former ΔG value refers to the formation of E4(N2), the latterto the formation of E4(NHNH) (ΔG = −17.7 or 19.9 kJ/mol atB3LYP level; SI Appendix, Fig. S7); the relative free energy of thesetwo states is within the computational error. Regardless of thisminor uncertainty, the present result is very important, as itclearly supports and illuminates the experimentally proposed remechanism by indicating that the formation of the diazene-level E4(2N2H) intermediates, in particular the diazene-bound in-termediate E4(NHNH), is indeed essentially thermoneutral asreported (8) and becomes thermodynamically accessible throughthe re/oa equilibrium process. This is a truly remarkable enzymatic

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achievement, as the noncatalytic direct hydrogenation of N2 toform diazene is endergonic by more than 200 kJ/mol (68).An explanation for the stability of the FeMo-co diazene-bound

intermediate E4(NHNH) is provided by the NBO analysis of thisstate (SI Appendix, Tables S14 and S15), which reveals that thediazene moiety interacts with FeMo-co via π(N=N) → d*(Fe2)and d*(Fe6) charge donation, and that these strong bonding in-teractions considerably stabilize this highly energetic species.Because of these strong interactions in the E4(NHNH) intermediatewith the Fe2 and Fe6 centers, the π character of the N–N bond ofthe diazene is lost and replaced with Fe–N bonds resulting from 3d(Fe) [with a smaller extent of s(Fe)] and p(N) mixing. This enablesthe stepwise protonation of the N2 moiety to yield first E4(H; N2H)and then E4(NHNH), during which the Fe2–N and Fe3–N in-teraction intensify and the Fe2–S2B bond breaks, with the sulfurpicking up a proton from α-195His. Upon removal of the N2H orNHNH fragments, the cluster returns to the E1(H) or E0 state,respectively, the Fe2–S2B bond is restored, and the proton isreturned to α-195His. We hypothesize that the hemilability of theFe–S bond is important for the overall catalytic efficiency: in ad-dition to facilitating the re of H2, it allows the formation of a Fe–Nbond and therefore helps stabilize the otherwise highly unstableN2H and NHNH intermediates. The NBO analysis of all of theE4(2N2H) states, quantifying the conclusions drawn above, issummarized in SI Appendix, Tables S14 and S15.

Discussion and ConclusionWe have carried out an extensive BS DFT study of N2 activationby nitrogenase. The analysis of structural models of the FeMo-coenvironment with a wide range of complexity reveals that theutilization of model (a), which incorporates the complete arrayof direct interactions of FeMo-co with its surrounding proteinenvelope, is required to give meaningful results, and to preventdisruption of FeMo-co that has accumulated 4[e−/H+], throughthe protonation of the central carbide. We find that this E4 stateexhibits a variety of low-lying isomers, with the lowest in energybeing E4(4H), which has two [Fe–H–Fe] bridging hydrides, asobserved in low-temperature ENDOR measurements (4) of thesingle conformer captured when the enzyme is freeze-trappedunder turnover conditions. Because of the single determinantnature of BS-DFT, these results provide only a qualitative ideaof the energy landscape of the possible E4 states. However, withthis in mind, the results are suggestive that at ambient temper-atures there may be a dynamic equilibrium among the four E4isomers, E4(4H), E4(4H)(b), E4(4H)(c), and E4(2H;H2). We alsofound that the re of H2 by E4(4H) to form the H2-bound complexE4(2H;H2) has a low barrier (ΔE‡ ∼ 22 kJ/mol). Although thisvalue represents a coarse approximation to true activation en-ergy, it is consistent with the experimental evidence and suggeststhat, at room temperature, E4(4H) and E4(2H;H2) should be infast equilibrium (Fig. 3), illuminating the recent finding that anH2 complex forms during re of the hydrides of E4(4H). Notably,we found that the re/oa equilibrium of Eq. 2, in which the loss ofH2 is coupled to N2 binding and the possible formation of adiazene-level intermediate E4(2N2H), in particular to the dia-zene E4(NHNH) intermediate itself, is nearly equi-ergic, in closeagreement with the recent direct measurement of this equi-librium (8). In this process, E4(4H) undergoes re of H2 butretains the H2 as the dihydrogen adduct E4(2H;H2), which can

revert to E4(4H) by oa of the H2; only after binding N2,forming E4(2H;H2;N2), does the enzyme release H2 and pro-ceed on to hydrogenated forms of N2. Indeed, any attempt toeliminate H2 directly from E4(2H;H2) failed. Instead, wefound a low barrier for the release of H2 from E4(2H;N2; H2)(ΔE‡ ∼ 28 kJ/mol).The thermodynamic analysis of N2 bond cleavage shows that,

although direct formation of E4(NHNH) without generation of H2is thermodynamically unfavorable, nitrogenase couples this un-favorable reaction of N2 with the highly favorable generation ofH2, resulting in an overall exergonic process to drive cleavage ofthe N≡N triple bond. However, thermodynamically, it is clearly farmore favorable to simply generate two H2 by hydride protonation,returning the enzyme to E0, than to generate only one H2 whilecarrying out the unfavorable N2 reduction. The key to catalyticnitrogen fixation by nitrogenase thus is the mechanistic couplingof the endergonic formation of E4(2N2H) to the exergonic releaseof one H2. That coupling of the two processes is captured in Fig. 5.The E4(4H) form(s) can undergo re of H2 to form E4(2H;H2),thereby capturing the free energy of H2 formation as reducingpower of this state’s doubly reduced FeMo-co. However, experi-ment shows this high-energy E4 state does not by itself release H2;if it did, D2 would react with the state produced, even in the ab-sence of N2, contrary to observation (16). As the present com-putations now show, it is the binding of N2 to the reductivelyactivated H2 complex E4(2H;H2) state that mechanistically cou-ples re of H2 to N2 reduction: N2 binding induces the loss of H2and leads to N2 reduction with formation of E4(NHNH) (Figs. 3and 5). Although the exergonic production of H2 provides thethermodynamic driving force for the endergonic cleavage of theN≡N triple bond, it is the mechanistic coupling of N2 binding withthe release H2 formed by re of the E4(4H) bridging hydrides that isthe true heart of the re mechanism of nitrogenase catalysis.

Supporting InformationPlease see SI Appendix for a schematic representation of the structuralmodels adopted in the present study; relative energy of possible spin con-figuration for the E0 state; representation of relevant En states; relativeenergies of BS solutions and spin populations for E0 and selected E4 states asobtained at BP86 and B3LYP level of theory; statistical data on the devia-tions from the crystal structure of Fe–Fe, Fe–C, and Fe–S distances in the E0state calculated using different exchange and correlation functionals;structural data of the En states; benchmark of DFT exchange and correlationfunctionals; analysis of the protein environment and stability of FeMo-co;natural bond orbitals analysis of selected E4 states; a discussion on the cal-culation of the energetics reported in Fig. 5; and Cartesian coordinates ofthe structures calculated in the present study. Please see Movie S1 for ananimation showing the mechanism for H2 re and N2 binding as inferred fromthe present study.

ACKNOWLEDGMENTS. We are grateful to Dr. R. Morris Bullock andDr. Michael T. Mock for stimulating discussions. We thank an anonymousreviewer for suggesting the analysis of the role of the protein environmenton the structure of FeMo-co in the E4 state. This work was supported by theUS Department of Energy (DOE), Office of Science, Basic Energy Sciences,Division of Chemical Sciences, Geosciences, and Bio-Sciences AwardDE-AC05-76RL01830/FWP66476 (to S.R. and L.C.S.), by National Institutes ofHealth Award GM 111097 (to B.M.H.), and by National Science FoundationAward MCB 1515981 (to B.M.H.). Computer resources were provided by theW. R. Wiley Environmental Molecular Sciences Laboratory, a DOE Office ofScience User Facility located at Pacific Northwest National Laboratory andsponsored by DOE’s Office of Biological and Environmental Research.

1. Eady RR (1996) Structure–function relationships of alternative nitrogenases. ChemRev 96:3013–3030.

2. Spatzal T, et al. (2011) Evidence for interstitial carbon in nitrogenase FeMo cofactor.Science 334:940.

3. Thorneley RN, Lowe DJ (1985) Kinetics and mechanism of the nitrogenaseenzyme system. Molybdenum Enzymes, ed Spiro TG (Wiley, New York), Vol 7, pp89–116.

4. Burgess BK, Lowe DJ (1996) Mechanism of molybdenum nitrogenase. Chem Rev 96:2983–3012.

5. Thorneley RNF, Lowe DJ (1996) Nitrogenase: Substrate binding and activation. J BiolInorg Chem 1:576–580.

6. Hoffman BM, Lukoyanov D, Yang Z-Y, Dean DR, Seefeldt LC (2014) Mechanism ofnitrogen fixation by nitrogenase: The next stage. Chem Rev 114:4041–4062.

7. Hoffman BM, Lukoyanov D, Dean DR, Seefeldt LC (2013) Nitrogenase: A draftmechanism. Acc Chem Res 46:587–595.

8. Lukoyanov D, et al. (2016) Reductive elimination of H2 activates nitrogenase to reducethe N≡N triple bond: Characterization of the E4(4H) Janus intermediate in wild-typeenzyme. J Am Chem Soc 138:10674–10683.

Raugei et al. PNAS | vol. 115 | no. 45 | E10529

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YBIOPH

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nloa

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ruar

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, 202

0

9. Lukoyanov D, et al. (2017) Photoinduced reductive elimination of H2 from the ni-trogenase dihydride (Janus) state involves a FeMo-cofactor-H2 intermediate. InorgChem 56:2233–2240.

10. Schimpl J, Petrilli HM, Blöchl PE (2003) Nitrogen binding to the FeMo-cofactor ofnitrogenase. J Am Chem Soc 125:15772–15778.

11. Kästner J, Blöchl PE (2007) Ammonia production at the FeMo cofactor of nitrogenase:Results from density functional theory. J Am Chem Soc 129:2998–3006.

12. Kästner J, Blöchl PE (2005) Towards an understanding of the workings of nitrogenasefrom DFT calculations. ChemPhysChem 6:1724–1726.

13. Kästner J, Hemmen S, Blöchl PE (2005) Activation and protonation of dinitrogen atthe FeMo cofactor of nitrogenase. J Chem Phys 123:074306.

14. Lovell T, Li J, Liu T, Case DA, Noodleman L (2001) FeMo cofactor of nitrogenase: Adensity functional study of states M(N), M(OX), M(R), and M(I). J Am Chem Soc 123:12392–12410.

15. Pelmenschikov V, Case DA, Noodleman L (2008) Ligand-bound S = 1/2 FeMo-cofactorof nitrogenase: Hyperfine interaction analysis and implication for the central ligand Xidentity. Inorg Chem 47:6162–6172.

16. Harris TV, Szilagyi RK (2011) Comparative assessment of the composition and chargestate of nitrogenase FeMo-cofactor. Inorg Chem 50:4811–4824.

17. Varley JB, Nørskov JK (2013) First-principles calculations of Fischer–Tropsch processescatalyzed by nitrogenase enzymes. ChemCatChem 5:732–736.

18. Varley JB, Wang Y, Chan K, Studt F, Nørskov JK (2015) Mechanistic insights into ni-trogen fixation by nitrogenase enzymes. Phys Chem Chem Phys 17:29541–29547.

19. Khadka N, et al. (2016) CO2 reduction catalyzed by nitrogenase: Pathways to formate,carbon monoxide, and methane. Inorg Chem 55:8321–8330.

20. Siegbahn PEM (2016) Model calculations suggest that the central carbon in the FeMo-cofactor of nitrogenase becomes protonated in the process of nitrogen fixation. J AmChem Soc 138:10485–10495.

21. Rao L, Xu X, Adamo C (2016) Theoretical investigation on the role of the centralcarbon atom and close protein environment on the nitrogen reduction in Mo nitro-genase. ACS Catal 6:1567–1577.

22. McKee ML (2016) A new nitrogenase mechanism using a CFe8S9 model: Does H2

elimination activate the complex to N2 addition to the central carbon atom? J PhysChem A 120:754–764.

23. Siegbahn PEM (2018) Is there computational support for an unprotonated carbon inthe E4 state of nitrogenase? J Comput Chem 39:743–747.

24. Siegbahn PEM (2018) A major structural change of the homocitrate ligand of prob-able importance for the nitrogenase mechanism. Inorg Chem 57:1090–1095.

25. Cao L, Caldararu O, Ryde U (2017) Protonation states of homocitrate and nearbyresidues in nitrogenase studied by computational methods and quantum refinement.J Phys Chem B 121:8242–8262.

26. Benediktsson B, Bjornsson R (2017) QM/MM study of the nitrogenase MoFe proteinresting state: Broken-symmetry states, protonation states, and QM region conver-gence in the FeMoco active site. Inorg Chem 56:13417–13429.

27. Bjornsson R, Neese F, DeBeer S (2017) Revisiting the Mössbauer isomer shifts of theFeMoco cluster of nitrogenase and the cofactor charge. Inorg Chem 56:1470–1477.

28. Sippel D, et al. (2018) A bound reaction intermediate sheds light on the mechanism ofnitrogenase. Science 359:1484–1489.

29. Ding S, et al. (2016) Hemilabile bridging thiolates as proton shuttles in bioinspired H2

production electrocatalysts. J Am Chem Soc 138:12920–12927.30. Ding S, Ghosh P, Darensbourg MY, Hall MB (2017) Interplay of hemilability and redox

activity in models of hydrogenase active sites. Proc Natl Acad Sci USA 114:E9775–E9782.

31. Morrison CN, Spatzal T, Rees DC (2017) Reversible protonated resting state of thenitrogenase active site. J Am Chem Soc 139:10856–10862.

32. Smith D, Danyal K, Raugei S, Seefeldt LC (2014) Substrate channel in nitrogenaserevealed by a molecular dynamics approach. Biochemistry 53:2278–2285.

33. Klamt A, Schüürmann G (1993) COSMO: A new approach to dielectric screening insolvents with explicit expressions for the screening energy and its gradient. J ChemSoc Perkin Trans 2 1993:799–805.

34. Becke AD (1988) Density-functional exchange-energy approximation with correctasymptotic behavior. Phys Rev A Gen Phys 38:3098–3100.

35. Perdew JP (1986) Density-functional approximation for the correlation energy of theinhomogeneous electron gas. Phys Rev B Condens Matter 33:8822–8824.

36. Perdew JP (1986) Erratum: Density-functional approximation for the correlation en-ergy of the inhomogeneous electron gas. Phys Rev B Condens Matter 34:7406.

37. Becke AD (1993) Density‐functional thermochemistry. III. The role of exact exchange.J Chem Phys 98:5648–5652.

38. Lee C, Yang W, Parr RG (1988) Development of the Colle-Salvetti correlation-energyformula into a functional of the electron density. Phys Rev B Condens Matter 37:785–789.

39. Stephens PJ, Devlin FJ, Chabalowski CF, Frisch MJ; Army Research Laboratory, Aber-deen Proving Ground, MD (1995) Ab Initio Calculation of Vibrational Absorption andCircular Dichroism Spectra Using Density Functional Force Fields (Defense TechnicalInformation Center, Fort Belvoir, VA). Available at www.dtic.mil/docs/citations/ADA291297. Accessed April 25, 2017.

40. Schäfer A, Horn H, Ahlrichs R (1992) Fully optimized contracted Gaussian basis sets foratoms Li to Kr. J Chem Phys 97:2571–2577.

41. Roy LE, Hay PJ, Martin RL (2008) Revised basis sets for the LANL effective core po-tentials. J Chem Theory Comput 4:1029–1031.

42. Ditchfield R, Hehre WJ, Pople JA (1971) Self‐consistent molecular‐orbital methods. IX.An extended Gaussian‐type basis for molecular‐orbital studies of organic molecules.J Chem Phys 54:724–728.

43. Valiev M, et al. (2010) NWChem: A comprehensive and scalable open-source solutionfor large scale molecular simulations. Comput Phys Commun 181:1477–1489.

44. Bjornsson R, et al. (2014) Identification of a spin-coupled Mo(III) in the nitrogenaseiron–molybdenum cofactor. Chem Sci 5:3096–3103.

45. Venters RA, et al. (1986) ENDOR of the resting state of nitrogenase molybdenum-ironproteins from Azotobacter vinelandii, Klebsiella pneumoniae, and Clostridium pas-teurianum. Proton, iron-57, molybdenum-95, and sulfur-33 studies. J Am Chem Soc108:3487–3498.

46. Lukoyanov D, Yang Z-Y, Dean DR, Seefeldt LC, Hoffman BM (2010) Is Mo involved inhydride binding by the four-electron reduced (E4) intermediate of the nitrogenaseMoFe protein? J Am Chem Soc 132:2526–2527.

47. Lukoyanov DA, et al. (2018) Hydride conformers of the nitrogenase FeMo-cofactortwo-electron reduced state E2(2H), assigned using cryogenic intra electron para-magnetic resonance cavity photolysis. Inorg Chem 57:6847–6852.

48. Noodleman L, Lovell T, Liu T, Himo F, Torres RA (2002) Insights into properties andenergetics of iron-sulfur proteins from simple clusters to nitrogenase. Curr Opin ChemBiol 6:259–273.

49. Shoji M, et al. (2006) Theory of chemical bonds in metalloenzymes V: Hybrid-DFTstudies of the inorganic [8Fe–7S] core. Int J Quantum Chem 106:3288–3302.

50. Shoji M, et al. (2006) Hybrid-density functional study of magnetism and ligand controlin Ni9 complexes. Chem Phys Lett 421:483–487.

51. Reiher M, Wiebe N, Svore KM, Wecker D, Troyer M (2017) Elucidating reactionmechanisms on quantum computers. Proc Natl Acad Sci USA 114:7555–7560.

52. Montgomery JM, Mazziotti DA (2018) Strong electron correlation in nitrogenasecofactor, FeMoco. J Phys Chem A 122:4988–4996.

53. Neese F (2017) High-level spectroscopy, quantum chemistry, and catalysis: Not just apassing fad. Angew Chem Int Ed Engl 56:11003–11010.

54. Barone V, Cossi M, Tomasi J (1997) A new definition of cavities for the computation ofsolvation free energies by the polarizable continuum model. J Chem Phys 107:3210–3221.

55. Grimme S (2004) Accurate description of van der Waals complexes by density func-tional theory including empirical corrections. J Comput Chem 25:1463–1473.

56. Grimme S, Antony J, Ehrlich S, Krieg H (2010) A consistent and accurate ab initioparametrization of density functional dispersion correction (DFT-D) for the 94 ele-ments H-Pu. J Chem Phys 132:154104.

57. Ehrlich S, Moellmann J, Reckien W, Bredow T, Grimme S (2011) System-dependentdispersion coefficients for the DFT-D3 treatment of adsorption processes on ionicsurfaces. ChemPhysChem 12:3414–3420.

58. Askerka M, Brudvig GW, Batista VS (2017) The O2-evolving complex of photosystem II:Recent insights from quantum mechanics/molecular mechanics (QM/MM), extendedX-ray absorption fine structure (EXAFS), and femtosecond X-ray crystallography data.Acc Chem Res 50:41–48.

59. Sproviero EM, Gascón JA, McEvoy JP, Brudvig GW, Batista VS (2008) Quantum me-chanics/molecular mechanics study of the catalytic cycle of water splitting in photo-system II. J Am Chem Soc 130:3428–3442.

60. Sproviero EM, Gascón JA, McEvoy JP, Brudvig GW, Batista VS (2007) Quantum me-chanics/molecular mechanics structural models of the oxygen-evolving complex ofphotosystem II. Curr Opin Struct Biol 17:173–180.

61. Buckel W, Thauer RK (2018) Flavin-based electron bifurcation, ferredoxin, flavodoxin,and anaerobic respiration with protons (Ech) or NAD+ (Rnf) as electron acceptors: Ahistorical review. Front Microbiol 9:401.

62. Burford RJ, Fryzuk MD (2017) Examining the relationship between coordinationmode and reactivity of dinitrogen. Nat Rev Chem 1:0026.

63. Henderson RA (1990) Activation of dinitrogen at binuclear sites. Transition Met Chem15:330–336.

64. Weinhold F (2002) Natural bond orbital methods. Encyclopedia of ComputationalChemistry, eds von Rague Schleyer P, et al. (Wiley, Chichester, UK).

65. Reed AE, Curtiss LA, Weinhold F (1988) Intermolecular interactions from a naturalbond orbital, donor-acceptor viewpoint. Chem Rev 88:899–926.

66. Cavigliasso G, Stranger R, Yates BF (2012) Dinitrogen metal complexes with a stronglyactivated N-N bond: A computational investigation of [(Cy2N)3Nb-(μ-NN)-Nb(NCy2)3]and related [Nb-(μ-NN)-Nb] systems. Dalton Trans 41:13948–13959.

67. Krishnamurthy VM, et al. (2008) Carbonic anhydrase as a model for biophysical andphysical-organic studies of proteins and protein-ligand binding. Chem Rev 108:946–1051.

68. Matus MH, Arduengo AJ, 3rd, Dixon DA (2006) The heats of formation of diazene,hydrazine, N2H3

+, N2H5+, N2H, and N2H3 and the methyl derivatives CH3NNH,CH3NNCH3, and CH3HNNHCH3. J Phys Chem A 110:10116–10121.

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